Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T14:50:15.274Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral Numerical Study of a Problem Governed by Navier-StokesEquations, Influence of Rayleigh and Prandtl Numbers

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
E. El Guarmah  and
A. Cheddadi
E. El Guarmah
Affiliation:
EMI, Mohamed V University Ibn Sina Str., POB 765 Agdal, Rabat, Morocco Royal Air School, Mathematics and Informatics Department, BEFRA, Marrakech, Morocco
A. Cheddadi
Affiliation:
EMI, Mohamed V University Ibn Sina Str., POB 765 Agdal, Rabat, Morocco
Get access

Abstract

We present in this work a numerical study of a problem governed by Navier-Stokesequations and heat equation. The mathematical problem under consideration is obtained bymodelling the natural convection of an incompressible fluid, in laminar flow between twohorizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposedto be greater than the outer one. The numerical simulation of the flow is carried out bycollocation-Legendre method. The influence of Prandtl and Rayleigh numbers isinvestigated

Keywords

Navier-Stokes equationsheat equationcollocation-Legendre methodCrank-Nicholson method
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9thInternational Conference on Numerical Analysis and Optimization , 2010 , pp. 23 - 28
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

C. Bernardi, Y. Maday. Approximations spectrales de problèmes aux limites elliptiques. Springer-Verlag France, Paris, 1992.
C. Canuto, M. Y. Hussaini, A. Quarteroni, T. Zang. Spectral methods in fluid dynamics. Springer, New York, 1988.
Cheddadi, A., El Guarmah, E.. Discrétisation spectrale d’un écoulement fluide à Prandtl infini dans une géométrie annulaire cylindrique . PCN Journal, Physical and Chemical News, 30 (2006), 42–48.Google Scholar
A. Cheddadi, E. El Guarmah. Influence of the collocation grid on a collocation-Chebyshev procedure for the numerical simulation of Navier-Stokes equations. AMSE Journal, Modelling and Simulation, Best of Book (2005), 127–136.
A. Cheddadi, M. C. Charrier-Mojtabi, A. Mojtabi. Étude comparative de la convection naturelle dans des espaces annulaires cylindriques fluide et poreux: 1-écoulements bidimensionnels multicellulaires. 6ème Colloque Maghrébin sur les modèles numériques de l’ingénieur (C2MNI6), Tunis, 24-26 Novembre 1998.
Crawford, L., Lemlich, R.. Natural convection in horizontal concentric cylindrical annuli . IEC Fundamentals, 1 (1962), 260–264.CrossRefGoogle Scholar
B. Fornberg. A practical guide to pseudo spectral methods. Cambridge University Press, 1996.
Gray, D., Giorgini, A.. The Validity of the Boussinesq approximation for liquids and gases . Int. J. Heat Mass Transfer, 19 (1976), 545–551.CrossRefGoogle Scholar
Kuehn, T. H., Goldstein, R. H.. An experimental and theoretical study of natural convection in the annulus between horizonatl concentric cylinders . J. Fluid, 74 (1976), 695–719.CrossRefGoogle Scholar
R. Peyret. Introduction to spectral methods. Computational Fluid Dynamics, Lecture Series Von Karman, 1986-04.
Quarteroni, A.. Blending Fourier and Chebyshev interpolation . J. Approx. Theory, 51 (1987), 115–126.CrossRefGoogle Scholar
M. Uhlmann. The need for de-aliasing in a Chebyshev pseudo-spectral method. Num. Meth. for Fluid Dynamics, (1986), 463–475.